# Make two expressions look alike OR check that they are the same

I would like to compare my Mathematica calulations with the results from a paper.

I get:

myRes= (b/g)^0.25 + (0.25*(b/g)^0.25*w[x])/g + (b*((-0.09375*b)/(b/g)^1.75 + (0.25*g)/(b/g)^0.75)*w[x]^2)/g^4 + (0.1171875*b^3*w[x]^3)/((b/g)^2.75*g^6) +
((0.12646484375*b^4)/((b/g)^3.75*g^8) - (0.03125*(b/g)^0.25)/g^4)*w[x]^4


The paper gets:

paperRes = b^0.25*(g^(-0.25) + (0.25*w[x])/g^1.25 + (0.15625*w[x]^2)/g^2.25 + (0.1171875*w[x]^3)/g^3.25 + (0.09521484375*w[x]^4)/g^4.25)


I want to be sure that those two expressions are actually the same. How can I do it ?

I already tried: Reduce[myRes==paperRes] but it does not seem to work

## 2 Answers

You need to assume that b > 0 and g > 0

myRes = (b/g)^0.25 + (0.25*(b/g)^0.25*w[x])/
g + (b*((-0.09375*b)/(b/g)^1.75 + (0.25*g)/(b/g)^0.75)*w[x]^2)/
g^4 + (0.1171875*b^3*w[x]^3)/((b/g)^2.75*
g^6) + ((0.12646484375*b^4)/((b/g)^3.75*g^8) - (0.03125*(b/g)^0.25)/
g^4)*w[x]^4 // Rationalize // Simplify[#, b > 0 && g > 0] &

(* (1/(2048 g^(17/4)))b^(
1/4) (2048 g^4 + 512 g^3 w[x] + 320 g^2 w[x]^2 + 240 g w[x]^3 + 195 w[x]^4) *)

paperRes =
b^0.25*(g^(-0.25) + (0.25*w[x])/g^1.25 + (0.15625*w[x]^2)/
g^2.25 + (0.1171875*w[x]^3)/g^3.25 + (0.09521484375*w[x]^4)/g^4.25) //
Rationalize // Simplify[#, b > 0 && g > 0] &

(* (1/(2048 g^(17/4)))b^(
1/4) (2048 g^4 + 512 g^3 w[x] + 320 g^2 w[x]^2 + 240 g w[x]^3 + 195 w[x]^4) *)

myRes == paperRes

(* True *)

• Wow, nice answer ! Thanks a lot!! – james Mar 28 '18 at 14:56

Very simple method: Just plot both functions for some chosen constants and see if they have the same shape. Of course, this is not a general proof that the functions are the same, but sometimes it is sufficient.

myRes= (b/g)^0.25 + (0.25*(b/g)^0.25*w[x])/g + (b*((-0.09375*b)/(b/g)^1.75 + (0.25*g)/(b/g)^0.75)*w[x]^2)/g^4 + (0.1171875*b^3*w[x]^3)/((b/g)^2.75*g^6) +
((0.12646484375*b^4)/((b/g)^3.75*g^8) - (0.03125*(b/g)^0.25)/g^4)*w[x]^4;

paperRes = b^0.25*(g^(-0.25) + (0.25*w[x])/g^1.25 + (0.15625*w[x]^2)/g^2.25 + (0.1171875*w[x]^3)/g^3.25 + (0.09521484375*w[x]^4)/g^4.25);

a = Plot[myRes /. {w[x] -> x, b -> 1, g -> 2}, {x, -10, 10}, PlotStyle -> {Blue, Thin}];
b = Plot[paperRes /. {w[x] -> x, b -> 1, g -> 2}, {x, -10, 10},
PlotStyle -> {Dotted, Red, Thickness[0.01]}];

Show[a,b] • Thanks. This is also a great method. – james Mar 28 '18 at 15:04